Analytical modelling and experimental validation of compliance-based low-frequency resonators for water circuits

Abstract

Transmission losses of compact compliance-based resonators in water circuits are investigated. Experiments are performed to measure the anechoic transmission losses (TLan) of flexible-plate resonators and a gas resonator designed for frequencies between 10 and 100 Hz. The measurements are compared to theoretical results based on a lumped-element model and a finite-element model. The TLan is measured using a robust form of the multi-microphone method, which gave identical results for open and closed pipe acoustic terminations at the transmission side of the setup. When an estimate of the reflection coefficient at the termination is known, good results are obtained with only one transmission-side microphone. When TLan is high, a single microphone is sufficient on each side. For the flexible-plate resonators the TLan measurements are in agreement with theory except close to resonance, where the transmission signals are below the detection limit. Due to assumptions of a rigid cavity wall and a clamped top-plate, the theoretical resonance frequencies are too high except for the thinnest plate which displays static deformation stiffening. This deformation stiffening limits the possibility to lower the resonance frequency by using a thin flexible plate in a circuit with high static pressure. Low resonance frequencies are easier to reach with a gas resonator, in which a piston separates the water from a volume filled with air. For the gas-resonator, the measurements agree with the theoretical predictions when assuming a significant damping. The friction between the air-water-separation piston and cavity wall is suspected to cause this damping. Theory predicts that the TLan of both resonators designed for same resonance frequencies in absence of losses are equivalent. They therefore have quite similar performances except close to the resonance frequency. The flexible-plate resonator has a higher quality factor and higher (TLan) around the resonance frequency. The gas resonator is more complex and needs more maintenance but allows fine tuning of the resonance frequency by varying the gas volume.